Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 3x + 1$ and $ KL = 9x - 29$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {3x + 1} = {9x - 29}$ Solve for $x$ $ -6x = -30$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 3({5}) + 1$ $ KL = 9({5}) - 29$ $ JK = 15 + 1$ $ KL = 45 - 29$ $ JK = 16$ $ KL = 16$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {16} + {16}$ $ JL = 32$